Jonas Hofmann has scored three goals in four matches for Germany
The visitors, undefeated in 12 games under Hansi Flick, needed a ninth-minute equaliser from Jonas Hofmann to earn a point.
Hungary opened the scoring when Zsolt Nagy drove a shot past Manuel Neuer after the German goalkeeper had parried the ball into his path.
Germany sit third in Group A3 behind Hungary and leaders Italy.
Flick's side, who have now drawn their last four consecutive matches 1-1, were jolted into action as the hosts took a surprise lead.
However, after Borussia Monchengladbach midfielder Hofmann had scored his third goal in four matches they struggled in front of goal despite monopolising possession.
Chelsea's Timo Werner failed to make an impact alongside club colleague Kai Havertz, with both withdrawn before the end.
Hungary ended the contest with six more efforts on target than the visitors.
-- Courtesy of BBC Sport